Pay freeze: How $2B + 1 decade = $60B

Some mathematicians’ skills go as far as subtracting how much change they should get back from the local fast-food joint from their $20 bill.

The rest of us are left wondering how the government will get $60 billion in savings in 10 years by saving $2 billion a year with a two-year freeze on federal employees’ wages.

Jeffrey Zients, federal chief performance officer and deputy director for management at the Office of Management and Budget, mathematized it for us this morning:

I’m going to make it sort of the simple version here. It’s a little more complicated because of how the numbers compound and all the rest. But let me just keep this simple.

The $2 billion for fiscal year '11 is actually about a $3 billion or so annual run rate. It’s $2 billion because the fiscal year starts Oct. 1 and pay is set on a calendar-year basis. So the $2 billion only captures 9/12 of the actual savings.

Obviously, in out-years, you get the benefit of the full annualized savings. So think of it as around $3 billion, the second year being around $3 billion on an annual basis, or $2 billion in actual fiscal year 2012. So take $3 billion plus roughly $3 billion — you’re at $6 billion. You do that for 10 years; that’s your $60 billion. For five years, it’s slightly less than half because of that nine-month piece for the first couple of years, and that’s how you get $28 billion for five years.

There you have it: $2 billion plus 10 years plus a two-year pay freeze can equal $60 billion in savings. But I guess it all depends on one term in the explanation: annual run rate. To reach the savings points, the government has to keep everything the same. Now that math problem comes down to percentages. What is the likelihood of a constant run rate for 10 years? A small percentage point.